1. Field of the Invention
The invention consists of a method for measuring the semi-major and semi-minor axes of the electric ellipse of an elliptically, circularly, or linearly polarized wave. This invention has application for measuring the line-of-sight of the direction of wave propagation, the mode of propagation, and other properties of an electromagnetic or plasma wave in the Earth's magnetosphere, ionosphere, and interplanetary space. The apparatus for the measurement consists of three orthogonal antennas and a radio receiver that are capable of measuring the amplitude and phase of three orthogonal components of a wave electric field. This will be referred to as a three-axis electric field measurement.
As discussed by Calvert [1995], the primary application of this invention is to measure the wave mode and direction of the echoes that are produced by a satellite radio sounder in the Earth's magnetosphere. In this application, the delay of the radio echoes that are produced by a radio transmitter at the ordinary and extraordinary-mode wave cutoff frequencies can be used to measure the distance and density of different regions of the Earth's magnetosphere. The key to this technique, however, is to be able to measure the direction of an incoming wave, since a satellite sounder requires measuring the direction in order to make sense of the echoes that it receives.
As discussed by Calvert [1998], the electric field of a monochromatic electromagnetic or plasma wave always traces out an ellipse, where the plane of the ellipse is referred to as the plane of polarization. This ellipse will be referred to as the wave electric ellipse. The propagation modes in a magnetized plasma, which consist of the two solutions of the wave equation, are also found to be characterized by a different ellipse axis ratio, orientation of the electric ellipse, and rotation sense of the wave electric field. Except for wave directions that are almost exactly perpendicular to the magnetic field, it can be shown that the wave polarization for the ordinary and extraordinary modes for a radio sounder in the magnetosphere turn out to be approximately circular and perpendicular to the wave direction. The direction of the line-of-sight of wave propagation for these two modes can then be measured from the perpendicular to the wave electric ellipse.
In measuring the Earth's magnetosphere by this method, it is also relevant to measure the wave propagation mode, since this is needed in order to calculate the distance of a radio echo from the echo delay that is measured by this technique. As discussed below, this can also be measured by measuring the rotation sense of the wave electric field from the relative orientation of the semi-major and semi-minor axes of the electric ellipse.
The situation is also quite different when the ordinary and extraordinary modes overlap and are received at the same time by a radio sounder, since this can produce a linear or nearly-linear polarization from which the wave direction cannot be measured by this method. In this case, however, it then becomes possible to measure the direction of propagation from the faraday rotation at two adjacent frequencies, as follows.
As discussed by Davies [1990], faraday rotation occurs as a result of the difference in the phase velocity of the ordinary and extraordinary modes. Since the polarization of these two modes are approximately circular, this difference in phase velocity causes a rotation of the electric ellipse in the plane of polarization of the ordinary and extraordinary waves. The rotation angle that is caused by faraday rotation is then given by Equation 8.8 of Davies, [1990], in which the angle of faraday rotation is found to be proportional to the integrated plasma density times the magnetic field strength divided by the frequency squared. This equation is: ##EQU1## where .OMEGA. is the angle of rotation of the major axis of the electric ellipse, c is the speed of light, f.sub.p, f.sub.H, and .theta. are the plasma frequency, cyclotron frequency, and wave angle along the wave path that produces an echo, and s is the round trip distance from the sounder to the point at which the wave reflection occurs. For a radio echo in the Earth's magnetosphere at 20 kHz, the rotation angle of faraday rotation turns out to be approximately 50 radians, corresponding to eight complete rotations of the electric ellipse. Using two frequencies that produce a difference in the faraday rotation angle, this method can then be used to measure the line-of-sight of the direction of wave propagation, along with the angle of Faraday rotation, from the relative orientation of the major axis of the electric ellipse at two adjacent frequencies.
The field of the invention therefore includes the methods for measuring the wave mode and wave propagation direction of an elliptically, circularly, or linearly polarized wave, and the field of application of this invention includes the satellite and ground-based measurements that have been used to study the Earth's magnetosphere, ionosphere, and interplanetary space.
2. Description of Prior Art
The idea for the current invention originated from a study by Calvert [1985] in which the phase of a wave that was measured on a rotating antenna was compared to the predicted phase for a wave that was traveling in different directions. This method was then used by the author and others to measure the direction of the source of the auroral kilometric radiation that accompanies the aurora, as described in a related paper by Huff et al. [1988]. This study then led to the concept of measuring the direction of a wave from the in-phase and quadrature components of the wave electric field, as discussed by Calvert, et al. [1995]. The theory for the current invention was then subsequently worked out by the author and submitted for publication to Radio Science on Jul. 9, 1998.
Previous studies of the Earth's ionosphere have used directive antennas and interferometric methods to measure the direction of an incoming wave. These methods are based upon measuring the direction of a wave from the differing phase of a wave that impinges on spaced antennas or different parts of the same antenna. These methods are therefore fundamentally different from measuring the orientation of the wave electric ellipse, since other than incidentally, these methods do not depend upon the orientation of the electric ellipse. These methods are widely described in the open literature, as discussed in Section 4.2.5 of Davies [1990].
A related method that has also been used to measure the direction of a wave relies upon measuring the amplitude of the wave signal that is detected on a rotating antenna. In this method, which has been referred to as the "spin null method," the amplitude null that is produced by the directivity pattern of a rotating antenna is used to measure the direction of a wave. This method thus also amounts to using a directive antenna, since the null in the directivity pattern of an antenna is simply another part of the directivity pattern of that antenna. This method is commonly used in satellite measurements because of the simplicity of using a single or multiple dipole antenna, as described by Fainberg, et al. [1972] and Knoll, et al. [1978].
U.S. Pat. No. 5,323,166 by Nguyen describes a method for reconstructing the wave electric vector by measuring the amplitudes of the electric vector in different directions. In its claims, this method requires a matrix analysis in order to determine the necessary and sufficient conditions to ensure that the measured amplitudes contain enough information to provide a unique measurement of the sinusoidally varying components of a wave electric field, whereas in the current method it is considered obvious that three orthogonal measurements of the electric field are sufficient to measure the direction and phase of an incoming wave.
U.S. Pat. No. 5,731,783 by Graham, et al. also describes a method for estimating the polarization of a radar signal from the amplitudes that are detected by an array of radar detectors having different sensitivies for different wave polarzations. As stated in the claims of this invention, the purpose of the method is to estimate the polarization of an incoming wave without reference to the phases of the signals that are produced by these measurements. This method is therefore not relevant to the current method in which the polarization of a wave is measured from the amplitude and phase of the wave signals that are measured on three orthogonal antennas.
U.S. Pat. Nos. 4,323,898 and 4,323,899 by Barnes, et al. describe a method for averaging the wave polarization of an incoming wave by measuring and averaging the Stokes parameters of a wave signal in order to detect a signal that is greater than a predetermined threshold signal. Although such averaging is not precluded by the current invention, signal averaging and comparison with a threshold are not considered relevant to the method of this invention.
U.S. Pat. No. 4,295,140 by Brockman also illustrates prior art in measuring faraday rotation. This patent, which describes a receiver system for measuring the faraday rotation of a satellite radio beacon, is the only patent that could be found that is based on measuring faraday rotation at radio frequencies. Other details of this method are also discussed in Chapter 8, Section 8.3 of Davies [1990].
The lack of patents on this topic is attributed to the unique nature of the measurements that need to be made by a satellite radio sounder in the Earth's magnetosphere, in which it is necessary to simultaneously measure the echo distance and direction of an incoming wave.